Final answer:
The underwriting cost of an IPO is calculated as the difference between what the public paid for the shares and what the firm received. For a firm issuing 38.6 million shares priced at $12.50 for the IPO and $19.30 to the public, with $270,000 in fees, the underwriting cost is $262.95 million.
Step-by-step explanation:
To calculate the underwriting cost of an IPO, we need to first understand what comprises it. The underwriting cost is essentially the difference between the amount the firm raises from the IPO and the total proceeds the firm receives. In this case, the question states that a firm issues 38.6 million shares at an IPO price of $12.50 per share, but the offering price to the public is $19.30 per share. Additionally, the firm incurs $270,000 in associated fees, including legal fees, SEC registration fees, and other administrative costs.
First, we calculate the total amount raised from the IPO by multiplying the number of shares by the IPO price: 38.6 million shares x $12.50 per share = $482.5 million. The total proceeds to the firm, after subtracting the fees, are $482.5 million - $270,000 = $482.23 million. However, the shares were sold to the public at $19.30 per share, which means the total value to the public is 38.6 million shares x $19.30 per share = $745.18 million.
Thus, the underwriting cost is the difference between what the public paid and what the firm received: $745.18 million (public payment) - $482.23 million (firm proceeds) = $262.95 million. It's worth noting that the stock price increased by 18% on the first day, but this does not directly affect the calculation of underwriting costs as they are associated with the IPO transaction itself.